Problem: Simplify the following expression: $x = \dfrac{2p^2 - 24p + 70}{p - 7} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $2$ , so we can rewrite the expression: $ x =\dfrac{2(p^2 - 12p + 35)}{p - 7} $ Then we factor the remaining polynomial: $p^2 {-12}p + {35} $ ${-7} {-5} = {-12}$ ${-7} \times {-5} = {35}$ $ (p {-7}) (p {-5}) $ This gives us a factored expression: $\dfrac{2(p {-7}) (p {-5})}{p - 7}$ We can divide the numerator and denominator by $(p + 7)$ on condition that $p \neq 7$ Therefore $x = 2(p - 5); p \neq 7$